Journal diffusion factors and their mathematical relations with the number of citations and with the impact factor

Abstract

If we fix a citing period and a cited period, the Rowlands Journal Diffusion factor (RJDF) is the number of different citing journals divided by the total number of citations. The Frandsen Journal Diffusion factor (FJDF) is the number of different citing journals divided by the total number of citeable articles. Hence the quotient: diffusion factor of Frandsen divided by the one of Rowlands is the impact factor IF (for the given time periods). This paper investigates the mathematical properties of RJDF and FJDF in function of the number of citations or of IF and shows the validity of some unexplained claims (based on data) given in “T.F.Frandsen. Journal diffusion factors – a measure of diffusion ? Aslib Proceedings 56(1), 5-11, 2004”. We show that, under reasonable mathematical conditions (expressed intuitively in Frandsen (2004)), the RJDF is a convexly decreasing function of the number of citations and a concavely increasing function of IF. We also show that ()rRJDF,IF0= implies ()rFJDF,IF0> where r denotes the correlation coefficient of Pearson.